I've been running hardy (the upcoming ubuntu LTS release) for a while now. After a kernel update, I noticed I couldn't build any packages anymore due to configure failing when checking if built binaries could be run. A bit of log reading, the error seemed to be: "mmap: permission denied", hmm.
The configure test there should be fairly trivial, but just to be sure, I made a little test program and compiled it. The compiler works just fine but the produced binary gave the same mmap-error, so it seemed the arm emulation was broken. After stracing the binary a bit, I saw that it tried to do mmap(..., 4096, ...), which failed.
The error appeared after a kernel upgrade, so I tried to find something related to mmap in /proc, and find did give me /proc/sys/vm/mmap_min_addr, which had 65536 in it. Running sudo sh -c 'echo 4096 > /proc/sys/vm/mmap_min_addr' was my first instinct and it did indeed fix the problem -- any larger value and the problem resurfaced.
So, if you're running ubuntu hardy (or linux 2.6.24(?)), you might hit this problem; and lowering the mmap_min_addr should help.